Let A be an n x n matrix that satisfies AAT = In. Prove that det(A)...

 

Transcribed Image Text:

Let A be an n x n matrix that satisfies AAT = In. Prove that det(A) = +1 or -1. A matrix A = Rnxn is called orthogonal if ATA = In. Find examples of 2 x 2 and 3 3 orthogonal matrices (exclude diagonal matrices). Let A be an n x n matrix that satisfies AAT = In. Prove that det(A) = +1 or -1. A matrix A = Rnxn is called orthogonal if ATA = In. Find examples of 2 x 2 and 3 3 orthogonal matrices (exclude diagonal matrices).